Oscillator and communication system using the same

ABSTRACT

A transfer impedance from input terminals of a resonator to output terminals of the resonator is larger than a driving-point impedance of the input terminals of the resonator at an oscillation frequency. The input terminals of the resonator are connected with the drain terminals of transistors Q 1  and Q 2  that are outputs of a differential amplifier, and the output terminals of the resonator are connected with gate terminals of the transistors Q 1  and Q 2  that are inputs of the differential amplifier. With this configuration, during the oscillating operation, the oscillation voltage amplitude of the gate terminals of the transistors Q 1  and Q 2  becomes larger than the oscillation voltage amplitude of the drain terminals. Therefore, it is possible to prevent the transistor, which is oscillating, from operating in a triode region, and suppress the deterioration of the Q-factor.

CLAIM OF PRIORITY

The present application claims priority from Japanese Patent ApplicationJP 2007-233853 filed on Sep. 10, 2007, the content of which is herebyincorporated by reference into this application.

FIELD OF THE INVENTION

The present invention relates to an oscillator and a communicationsystem using the same, and particularly, to an LC cross-coupledoscillator that is suitable for generating a carrier wave signal of acommunication system and a radar system of a resonator microwave or amillimeter wave frequency band, and a communication system using thesame.

BACKGROUND OF THE INVENTION

An example of the LC cross-coupled oscillator that includes a resonatorconfigured by an inductor and a capacitor is disclosed inJP-A-2004-260301. Further, in D. B. Leeson, “A Simple Model of FeedbackOscillator Noise Spectrum”, Proc. IEEE, vol. 54, pp. no. 2, 329-330,February 1966, a phase noise power of an oscillator in a small signalmodel is disclosed. Further, in A. Hajimiri and T. H. Lee, “A generaltheory of phase noise in electrical oscillators” IEEE J. Solid-StateCircuits, vol. 33, pp. 179-194, February 1998, a phase noise power inthe large signal model is disclosed. Furthermore, an example of anoscillator in which the tail current source is removed from an LCcross-coupled oscillator and a common ground point of a differentialamplifier is directly connected with a circuit ground is disclosed inPing-Chen Huang, “A 131 GHz Push-push VCO in 90-nm CMOS Technology”,IEEE RFIC, 2005. An example of an LC cross-coupled oscillator that doesnot have a tail current source is described in T. Song, “A 5 GHzTransformer-Coupled CMOS VCO Using Bias-Level Shifting Technique”, IEEERFIC 2004.

SUMMARY OF THE INVENTION

The phase noise is an important indicator that represents theperformance of an oscillator. The output spectrum of an ideal oscillatoris exemplified by a line spectrum, but the spectrum of an actualoscillator has a skirt characteristic when the oscillation frequencyextends at both sides. The phase noise is defined as the ratio of anoscillation output level of the oscillation frequency and a noise levelof a frequency that is different from the oscillation frequency by apredetermined frequency. The characteristic of the phase noise isregarded as the most important characteristic because it is required tomaintain the quality of the communication system and transmitinformation without an error.

According to the above-mentioned D. B. Leeson, the phase noise power ofan oscillator in the small signal model is represented by the followingEquation 1.

$\begin{matrix}{{S\left( {\Delta\; f} \right)} \approx {{10{{Log}\left\lbrack {1 + {\frac{1}{\Delta\; f_{2}}\left( \frac{f_{0}}{2Q} \right)^{2}} + {\frac{fc}{\Delta\; f^{3}}\left( \frac{f_{0}}{2Q} \right)^{3}}} \right\rbrack}} + {10{Log}\;\frac{FvKT}{P_{0}}}}} & (1)\end{matrix}$

Here, fc, Δf, Q, P₀, and Fv indicate an oscillation frequency, an offsetfrequency from fc, a quality factor of a resonator, an oscillationpower, and a noise factor of the oscillator, respectively. The noisefactor represents a level of a noise component that is generated in theoscillator, and is caused by a transistor or a resistive component thatgenerates a thermal noise. Basically, Fv depends on the number oftransistors and the number of resistors in a circuit. In the case of anoscillator mounted in an integrated circuit, a channel thermal noisethat is generated from the transistor serves as the main factor amongthe noise components that are involved in Fv.

On the other hand, according to the above-mentioned A. Hajimiri and T.H. Lee, the phase noise power in the large signal model is representedby Equation 2.

$\begin{matrix}{{S\left( {\Delta\;\omega} \right)} = {10{{Log}\left\lbrack \frac{\underset{\_}{\overset{\_}{\,^{i_{n}^{2}}}}{\sum\limits_{n = 0}^{\infty}c_{n}^{2}}}{4q_{\max}^{2}\Delta\;\omega^{2}} \right\rbrack}\mspace{14mu}\left( {n\mspace{14mu}{is}\mspace{14mu}{an}\mspace{14mu}{integer}} \right)}} & (2)\end{matrix}$

Here, q_(max), i_(n), and C_(n) indicate the amount of maximum storedcharges at an oscillation node, the amount of injected noise current,and a Fourier coefficient when the oscillation waveform is Fourierseries expanded, respectively.

The q_(max) and i_(n) are parameters that relate to Po and Fv in theabove-mentioned Equation 1. As q_(max) becomes larger and i_(n) becomessmaller, the phase noise is improved. Here, C_(n) is a coefficient thatrepresents a distortion component of the oscillation waveform. In thecase of an ideal sine wave without distortion, if n>1, C_(n) is 0.Further, in the case of an actual electronic oscillator, if n>1, C_(n)is not 0 by the influence of the nonlinearity of the transistor. It isapparent from Equation 2 that when C_(n) is small, that is, thedistortion of the oscillation waveform is small, the phase noise isimproved.

According to Equations 1 and 2, the following four factors are importantto reduce the phase noise: (1) increase in oscillation amplitude, (2)increase in Q of a resonator, (3) reduction of the noise factor causedby the thermal noise of a transistor and a resistor, and (4) lowering ofthe distortion of an oscillation waveform.

FIG. 18 is a circuit diagram showing an example of a LC cross-coupledoscillator according to the related art. This oscillator includes adifferential amplifier circuit that includes Q1 and Q2, and a load thatincludes an LC resonator 1. An output signal of the differentialamplifier circuit is extracted from a drain terminal, and a frequency ofthe output signal is selected and amplified by an LC resonator 1 thathas a resonant frequency adjusted to a desired oscillation frequency.Thereafter, the output signal is input to a gate terminal of anothertransistor. The oscillation operation may be generated and maintainedwith a desired frequency by repeating this operation. A tail currentsource I1 that is connected with a common ground part of thedifferential amplifier circuit suppresses the amplitude of theoscillation signal to a constant value during the oscillating operationand reduces the distortion of the oscillation waveform.

On the other hand, FIG. 19 shows an oscillator that excludes the tailcurrent source from the LC cross-coupled oscillator of FIG. 18, anddirectly connects the common ground point of the differential amplifierwith a circuit ground. When the oscillator is configured as above, sincethe voltage drop does not occur in the tail current source, theamplitude becomes larger than that of the oscillator shown in FIG. 18.Moreover, since the transistors and the resistors that configure thetail current source are excluded, the noise factor of the oscillator canbe lowered. As a result, two of the above-described four factors, thatis, (1) increase in oscillation amplitude and (3) reduction of the phasenoise according to the reduction of the noise source are effective inreducing the phase noise.

However, two problems exist in the oscillator shown in FIG. 19. Theseproblems will be described with reference to FIG. 20. FIG. 20 showstypically a gate-drain voltage and a drain current during an oscillationoperation of the oscillator. As shown in FIG. 20, the dotted line 10indicates the boundary between a triode region and a saturation regionof a transistor and the condition is shown by Equation 3.V _(DS) ≧V _(GS) −V _(TH)  (3)

In the saturation region, the drain current is not effected by thedrain-source voltage. Therefore, the output resistance in the saturationoperating region is high. On the other hand, in the triode region, thedrain current is almost linearly proportional to the drain-sourcevoltage. Therefore, the output resistance in the triode region is low.The solid line 11 in FIG. 20 indicates the characteristics of a drainvoltage and a drain current: line 11(a) indicates that V_(gs) is small,line 11(b) indicates that V_(gs) is medium, and line 11(c) indicatesthat V_(gs) is large.

Reference numeral 40 in FIG. 20 denotes the characteristic of thegate-drain voltage and a drain current of a transistor during theoscillation operation of the cross-coupled oscillator shown in FIG. 18.The oscillator shown in FIG. 18 has a small oscillation amplitude asshown by the characteristic 40 due to the constant current of the tailcurrent source I1 and the amount of voltage drop of the tail current, asdescribed above. As a result, the oscillation waveform has lowdistortion. In the meantime, since the oscillator shown in FIG. 19 doesnot include the tail current source I1, the gate-source voltage thatcontrols the drain current serves as the magnitude of the oscillationamplitude voltage. Further, as shown by the characteristics 30, thegate-source voltage does not reach the saturation region of an MOStransistor, but enters the triode region. FIG. 21 shows transientwaveforms of a gate terminal VG and a drain terminal VD and a transientwaveform of a drain current ID of the oscillator shown in FIG. 19. Theoutput resistance of the transistor can be represented by the amount ofchanged drain current according to the change of the output voltage asdescribed above. The smaller the amount of change is, the larger theoutput resistance is. As known from the drain voltage and drain currentcharacteristics 11 shown in FIG. 20, the output resistance of the MOStransistor in the triode region (linear operation region of FIG. 21)remarkably decreases as compared with the output resistance in thesaturation region. In the LC cross-coupled oscillator, the outputresistance of the transistor is connected with a resonator 1 inparallel. Generally, the output resistance in the triode region issmaller than an impedance of the resonator 1 at a resonant frequency,that is, the oscillation frequency. Therefore, the resonant impedance islowered to deteriorate a Q-factor. Further, the periodic change inimpedance causes the distortion of the oscillation waveform. As aresult, the oscillator of FIG. 19 can obtain the effects, such as (1)increase in oscillation amplitude and (3) reduction of the noise factorFv to improve the phase noise, but problems, such as (2) increase in Qof a resonator and (4) distortion of an oscillation waveform alsoremain. Therefore, the oscillator is ineffective for reducing the phasenoise.

FIG. 22 shows an oscillator in which the tail current source I1 of theLC cross-coupled oscillator shown in FIG. 18 is disposed at a powersupply voltage VDD side. In this oscillator, even though a common sourceterminal of a differential pair is directly connected to a ground, aconstant current is supplied from a top current source. Therefore, theoperation principle has the same problems as the oscillator shown inFIG. 18.

FIG. 23 is an oscillator that has a DC component cut from a drain outputterminal of a transistor by a capacitor C3, input to a gate terminal ofanother transistor, and then bias-shifted to the gate terminal with adirect current that is lower than a direct current of the drain outputterminal in the LC cross-coupled oscillator that does not have the tailcurrent source shown in FIG. 19. Further, a signal attenuation circuit 7may be inserted between the capacitor C3 and the gate terminal. Anexample of the above described oscillator is disclosed in T. Song.

According to the example of FIG. 23, by lowering a bias voltage of thegate terminal, as shown by the characteristics 40 shown in FIG. 20, eventhough the amplitude voltage of the drain terminal becomes larger, thecondition of the saturation region represented by Equation 3 can besatisfied, which makes it possible to prevent the transistor fromoperating in the triode region of the transistor.

The above-described LC cross-coupled oscillator shown in FIG. 23 isconnected from the drain terminal to which a resonator is connected, toa gate of another transistor through a capacitive element C3 or anattenuator 7. Therefore, the oscillation amplitude in the gate terminalbecomes smaller than the oscillation amplitude of the drain terminal.

However, according to the cross-coupled amplifier of FIG. 23 in whichthe amplitude of the gate terminal is small (that is, the gate-sourcevoltage is small), a tail current source I1 is excluded, and thedistortion of the output amplitude is lowered without deteriorating theQ-factor, which improves the phase noise. However, there is stillproblem in that the phase noise effect followed by the increase in theamplitude can not be obtained. That is, the oscillator shown in FIG. 23can solves two among the factors to improve the phase noise, that is,(3) reduction of the noise factor Fv and (4) lowering of the distortionof an oscillator waveform, but the trade-off relationship that (1) theoscillation amplitude is decreased may be caused.

An object of the invention is to provide an LC cross-coupled oscillatorin which a common source terminal of a differential pair is directlyconnected to a ground, which is capable of increasing the oscillationamplitude of the gate terminal and lowering the distortion of theoscillation amplitude without deteriorating the Q-factor of theresonator, which results in increasing the oscillation amplitude,reducing the noise factor Fv, and reducing the distortion of theoscillation waveform. Thereby, it enables to provide an oscillatorhaving an excellent low phase noise characteristic and a communicationsystem using the same.

According to an exemplary embodiment of the invention, an oscillatorcomprising: a differential amplifier that includes a pair of transistorscommonly grounded; and a pair of resonators each of which includes afirst terminal, a second terminal, and a third terminal, wherein each ofthe resonators is configured by a feedback loop in which the firstterminal is connected to an output terminal of one of the transistors ofthe differential amplifier, and the second terminal is connected to aninput terminal of the other transistor of the differential amplifier,and wherein, in each of the resonators, a transfer impedance from thefirst terminal connected to the output terminal of the one transistor tothe second terminal connected to the input terminal of the othertransistor is larger than a driving-point impedance of the firstterminal at an oscillation frequency.

According to the exemplary embodiment of the invention, it is possibleto simultaneously satisfy the increase in the oscillation amplitude, theremoval of the tail current source (or top current source) that servesas the noise source, and reduction of the distortion of the oscillationwaveform without deteriorating the Q-factor which cause the trade-offrelationship with the related art, thereby achieving an oscillator thathas a low phase noise characteristic and a communication system usingthe same.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a circuit diagram showing a circuit configuration of anoscillator according to a first embodiment of the present invention;

FIG. 2 is a diagram showing the correspondence between a gate-drainvoltage and a drain current of the oscillator according to the firstembodiment of the invention;

FIG. 3 is a diagram showing an SNR of an output current with respect toa gate-source voltage of a transistor of the oscillator according to thefirst embodiment of the invention;

FIG. 4 is a circuit diagram showing a circuit configuration of anoscillator according to a second embodiment of the invention;

FIG. 5A is a verification circuit diagram for a resonator of the secondembodiment of the invention;

FIG. 5B is a diagram showing a frequency characteristic of the resonatorshown in FIG. 5A;

FIG. 5C is a diagram showing a frequency characteristic of the resonatorshown in FIG. 5A;

FIG. 6 is a diagram showing a transient waveform of the secondembodiment of the invention;

FIG. 7 is a circuit diagram showing a circuit configuration of anoscillator according to a third embodiment of the invention;

FIG. 8 is a diagram showing a frequency characteristic of a resonator ofthe third embodiment of the invention;

FIG. 9 is a diagram showing a transient waveform of the third embodimentof the invention;

FIG. 10 is a circuit diagram showing an oscillator according to amodification of the third embodiment of the invention;

FIG. 11 is a circuit diagram showing a circuit configuration of anoscillator according to a fourth embodiment of the invention;

FIG. 12A is a circuit diagram for verifying a resonator that composesthe fourth embodiment of the invention;

FIG. 12B is a diagram showing a frequency characteristic in theverification circuit diagram for the resonator shown in FIG. 12A;

FIG. 12C is a diagram showing a frequency characteristic of theresonator shown in FIG. 12A;

FIG. 13A is a diagram showing an example of a layout when the oscillatorshown in FIG. 10 is integrated in an IC chip;

FIG. 13B is a diagram showing an example of a layout when the oscillatorshown in FIG. 11 is integrated in an IC chip;

FIG. 14 is a circuit diagram showing an oscillator according to amodification of the fourth embodiment of the invention;

FIG. 15 is a circuit diagram showing a circuit configuration of anoscillator according to a fifth embodiment of the invention;

FIG. 16 is a diagram showing a frequency characteristic of a resonatorof the fifth embodiment of the invention;

FIG. 17 is a circuit diagram showing a circuit configuration of anoscillator according to a sixth embodiment of the invention;

FIG. 18 is a circuit diagram showing an oscillator according to a firstrelated (prior) art;

FIG. 19 is a circuit diagram showing an oscillator according to a secondrelated art;

FIG. 20 is a diagram showing a correspondence between a gate-drainvoltage and a drain current in the oscillator according to the secondrelated art;

FIG. 21 is a diagram showing transient voltage waveforms of a gateterminal and a drain terminal and a transient waveform of a draincurrent in the oscillator shown in FIG. 19;

FIG. 22 is a circuit diagram showing an oscillator according to a thirdrelated art; and

FIG. 23 is a circuit diagram showing an oscillator according to a fourthrelated art.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Hereafter, exemplary embodiments of the present invention will bedescribed in detail with reference to the accompanying drawings.

First Embodiment

FIG. 1 is a circuit diagram showing a circuit configuration of anoscillator according to a first embodiment of the invention. Theoscillator according to the first embodiment includes a differentialamplifier 2 that has two transistors Q1 and Q2 commonly grounded and apair of resonators 3A and 3B. Each of the resonators 3A and 3B includesa plurality of capacitors (C) and an plurality of inductors (L),respectively. Each resonator 3A and 3B has at least three terminals,that is, a first terminal, a second terminal, and a third terminal. Thefirst terminals are input terminals n-d1 and n-d2 to input an outputcurrent from the differential amplifier 2. The second terminals areoutput terminals n-g1 and n-g2 to drive the differential amplifier 2using a voltage. Further, the third terminals are connected to a powersupply of the oscillator, and include power supply direct connectionterminals n-p1 and n-p2 that directly connect at least some of theelements of the differential amplifier 2 to a power supply VDD and powersupply connections n-a1 and n-a2 that connect other elements of thedifferential amplifier 2 to the power supply or an AC ground.

The oscillator of the first embodiment connects an output of one of thetransistors (for example, Q1) that composes the differential amplifier 2to an input terminal (for example, n-d1) of one of the resonators (forexample, 3A), and input an output terminal (for example, n-g1) of theresonator to another transistor (for example, Q2) of the differentialamplifier, which refers to a feedback loop.

When the transistors Q1 and Q2, which compose the differentialamplifier, are embodied by a CMOS process, the output of thedifferential amplifier 2 serves as a drain terminal, an input serves asa gate terminal, and a common ground point serves as a source terminal.

The common source terminal of the differential amplifier 2, whichcomposes the oscillator is directly connected with the ground. The powersupply direct connection terminals n-p1 and n-p2 are directly connectedto the power supply VDD without interposing the tail current sourcetherebetween. Even though the power supply direct connection terminalsn-p1 and n-p2 are directly connected to the power supply, the terminalsdo not need to be directly connected to the power supply VDD, and may beconnected to the power supply with other component therebetween.Otherwise, the terminals may be connected to an AC ground point to besupplied with a voltage that is different from the power supply VDD.

The oscillator according to the first embodiment is configured such thata transfer impedance from the input terminals n-d1 and n-d2 of theresonator 3 to the output terminals n-g1 and n-g2 of the resonator 3(the pair of the resonators 3A and 3B) is larger than a driving-pointimpedance of the input terminals n-d1 and n-d2 at an oscillationfrequency. In this case, the input terminals n-d1 and n-d2 of theresonator are connected with the drain terminals of the transistors Q1and Q2 that serve as an output of the differential amplifier 2, and theoutput terminals n-g1 and n-g2 of the resonator 3 are connected with theinputs of differential amplifier 2 (gate terminals of the transistors Q1and Q2). Therefore, during the oscillating operation, the oscillationvoltage amplitude Vg of the gate terminals of the transistors Q1 and Q2becomes larger, while the oscillation voltage amplitude Vd of the drainterminals is small. Moreover, in order to remove the tail current source(or top current source) that serves as a noise source, as a connectionterminal of the resonator that is connected to the power supply, thepower supply direct connection terminals n-p1 and n-p2, which aredirectly connected to the power supply VDD without interposing the tailcurrent source therebetween, are provided.

With the above-described characteristics, in the oscillator according tothe present invention, the oscillation voltage amplitude of the gateterminals of the transistors Q1 and Q2 is larger than the oscillationvoltage amplitude of the drain terminals during the oscillatingoperation.

Therefore, according to the oscillator having the above characteristics,the gate terminal voltage amplitude of the transistors Q1 and Q2 thatconfigures the differential amplifier can become larger than the drainterminal voltage amplitude at a predetermined oscillation frequency. Asa result, it is possible to prevent the transistor, which isoscillating, from operating in a triode region, and deterioration of theQ-factor. Further, the gate terminal voltage amplitude can be maintainedto be equal with that of the LC cross-coupled oscillator that does nothave the tail current source. As described above, the oscillatoraccording to the first embodiment can obtain an excellent phase noisecharacteristic.

According to the oscillator of the first embodiment, it is furtherpossible to decrease the triode region operation during the oscillatingoperation of the transistor that composes the differential circuitaccording to the above-mentioned related art. This principle will bedescribed with reference to FIG. 2. A characteristic 50 of FIG. 2 showsa waveform and a magnitude of a voltage of the drain terminal of theoscillator according to the first embodiment. The oscillator accordingto the first embodiment makes it possible to reduce the triode regionoperating time of the transistor without adjusting the DC voltage levelof the gate terminal by reducing the voltage amplitude of the drainterminal.

By following this operating principle, it is possible to suppress thedeterioration of the Q-factor that is caused by the reduction of theoutput resistance of a transistor during the triode region operating.

As a result, it is possible to prevent the transistor, which isoscillating, from operating in the triode region, suppress thedeterioration of the Q-factor, and make the amplitude of the gateterminal be equal with that of the LC cross coupled oscillator that doesnot have a tail current source. With this above-described result, theoscillator according to the first embodiment can have a preferable phasenoise characteristic.

It is further possible to make the amplitude of the oscillating voltageof both gate terminals of the differential amplifier be equal to that ofthe LC cross coupled oscillator that does not have the tail currentsource while suppressing the deterioration of the Q-factor and increasethe SNR of the drain current. In addition, since there are no tailcurrent source and the top current source that serve as the noisesource, the noise factor Fv in Equation 1 by the above mentioned Leesoncan be reduced.

Hereafter, it will be described in detail. In the LC cross coupledoscillator, a signal current with respect to the gate voltage V_(GS) anda root-mean-square current I_(noise) of the channel thermal noise of thetransistor will be represented by the following Equations 4 and 5.

$\begin{matrix}{I_{signal} = {K_{0}\frac{W}{L}\left( {V_{gs} - V_{th}} \right)^{2}}} & (4) \\{\overset{\_}{I_{noise}} = {2\sqrt{{kT}\;\gamma\; g_{m}}}} & (5)\end{matrix}$

Here, K₀, W, L, K, T, and g_(m) indicate a transconductance parameter, atotal gate width, a gate length, the Boltzmann's constant, the absolutetemperature, and a transconductance, respectively. Further, γ is acoefficient of the channel thermal noise and becomes about ⅔ in thelong-channel device. The transconductance g_(m) is represented by thefollowing Equation 6.

$\begin{matrix}{g_{m} = {2K_{0}\frac{W}{L}\left( {V_{gs} - V_{th}} \right)}} & (6)\end{matrix}$

Here, if Equation 6 is substituted for Equation 5, I_(noise) isrepresented by following Equation 7.

$\begin{matrix}{\overset{\_}{I_{noise}} = {2\sqrt{2{kT}\;\gamma\; K_{0}\frac{W}{L}\left( {V_{gs} - V_{th}} \right)}}} & (7)\end{matrix}$

If the ratio of Equation 4 and Equation 7 is taken to derive thesignal-to-noise ratio (SNR), the following Equation 8 will be obtained.

$\begin{matrix}{{SNR} = {\frac{I_{signal}}{I_{noise}} = {\frac{1}{2}{\sqrt{\frac{K_{0}}{2{KT}\;\gamma} \cdot \frac{W}{L}} \cdot \left( {V_{gs} - V_{th}} \right)^{\frac{3}{2}}}}}} & (8)\end{matrix}$

According to Equation 8, the SNR of the MOS transistor is improved tohave a three-halves power of V_(GS).

The characteristic 400 of FIG. 3 shows the simulation result that takesthe SNR with respect to a gate voltage of the MOS transistor at apredetermined element value. It is further confirmed that the SNR isimproved according to the increase in the gate voltage, from thesimulation result of the characteristic 400.

Therefore, according to the first embodiment, it is possible tosimultaneously satisfy the increase in the oscillation amplitude, theremoval of the tail current source that serves as the noise source, andreduction of the distortion of the oscillation waveform withoutdeteriorating the Q-factor of the resonator, thereby achieving anoscillator that has a low phase noise characteristic.

The resonator 3 that is used for the oscillator according to the firstembodiment includes a plurality of capacitors (C) and a plurality ofinductors (L), respectively. However, each of capacitors and inductorsmay be configured by an open stub and a short stub that are installedfor the impedance matching of transmission lines such as a microstripline or a coplanar waveguide. Moreover, at least a part of theabove-mentioned capacitor and the inductor may be configured by using aparasitic element that is obtained by circuit wiring lines of an elementor between elements such as transistors.

The output of the oscillator according to the first embodiment may beany one of the drain terminal and the gate terminal of the differentialamplifier that composes the oscillator, or both of them.

Even though the oscillator according to the first embodiment includes anMOS transistor, it may include a bipolar transistor.

The example of the oscillator according to the first embodiment will bedescribed in more detail using the drawings as follows.

Second Embodiment

FIG. 4 is a circuit diagram showing an oscillator according to a secondembodiment of the invention. The oscillator according to the secondembodiment includes a differential amplifier 2, and a pair of resonators3A, 3B that have inductors L (Ls, Lp), and capacitors C (Cs, Cp). Eachresonator 3A and 3B includes parallel resonator units 60A and 60B thatincludes an inductor Lp and a capacitor Cp installed between terminals101 d 1 and 101 d 2 and terminals 101 c 1 and 101 c 2, and seriesresonator units 70A and 70B that include the inductor Ls and thecapacitor Cs arranged in this order as seen from the terminals 101 d(101 d 1, 101 d 2). The central points of the inductor Ls and thecapacitor Cs of the series resonator unit become terminals 101 g 1 and101 g 2. The terminals 101 c 1 and 101 c 2 are one of the thirdterminals in FIG. 1, and are connected with a power supply VDD or an ACground of the oscillator. The output terminal of the transistor Q1 thatcomposes the differential amplifier 2 is connected with an inputterminal 101 d 1 of the resonator 3A. An output of the resonator 3A isoutput from the terminal 101 g 1 and input to the input terminal of theother transistor Q2. An output of the transistor Q2 is connected withthe input terminal 101 d 2 of the resonator 3B, similar to thetransistor Q1 and the output of the resonator 3B is output from theterminal 101 g 2 to be input to the input terminal of transistor Q1. Theparallel resonator units 60A and 60B are provided with power supplydirect connection terminals 101 p 1 and 101 p 2 and second power supplyconnection terminals 101 a 1 and 101 a 2 as connection terminals to thepower supply VDD. The series resonator units 70A and 70B are providedwith connection terminals 101 b 1 and 101 b 2 that are one of the thirdterminals, as connection terminals to the power supply VDD. The powersupply direct connection terminals 101 p 1 and 101 p 2 directly connectat least the inductor Lp of the parallel resonator unit 60 to the powersupply VDD without interposing a tail current source therebetween.Therefore, the current that is supplied to the inductor Lp is notlimited, which avoids limiting the output of the resonator by the tailcurrent source. Meanwhile, a voltage that is different from the powersupply voltage, for instance, a bias voltage may be applied to thesecond power supply connection terminals 101 a 1 and 101 a 2 or otherconnection terminals 101 b 1 and 101 b 2.

The frequency characteristic of the resonator 3 will be described withreference to FIGS. 5A, 5B, and 5C. FIG. 5A is a verification circuitdiagram showing the AC characteristic of the resonator 3 according tothe second embodiment. The following Equation represents the AC voltageamplitudes Vd and Vg of the terminals 101 d and 101 g when thealternating current I_(in) is input from the terminals 101 d shown inFIG. 5A.

That is, the following Equation 9 represents the driving-point impedanceof the terminal 101 d when the AC source is connected between theterminals 101 d and 101 c of the resonator 3, Equation 10 represents atransfer impedance from the terminal 101 d to terminal 101 g.

$\begin{matrix}{V_{d} = {\frac{{\left( {\frac{1}{\omega\; C_{s}} - {\omega\; L_{s}}} \right)} \cdot \frac{L_{p}}{C_{p}}}{{j\left( {\frac{L_{p}}{C_{p}} + \frac{L_{p}}{C_{s}} + \frac{L_{s}}{C_{p}}} \right)} - {j\left( {{\omega^{2}L_{p}L_{s}} + \frac{1}{\omega^{2}C_{p}C_{s}}} \right)}} \cdot I_{i\; n}}} & (9) \\{V_{g} = {\frac{{\frac{1}{\omega\; C_{s}}} \cdot \frac{L_{p}}{C_{p}}}{{j\left( {\frac{L_{p}}{C_{p}} + \frac{L_{p}}{C_{s}} + \frac{L_{s}}{C_{p}}} \right)} - {j\left( {{\omega^{2}L_{p}L_{s}} + \frac{1}{\omega^{2}C_{p}C_{s}}} \right)}} \cdot I_{i\; n}}} & (10)\end{matrix}$

Even though the resistive component of the inductor and capacitor isomitted in Equations 9 and 10 for the sake of simplicity, it is notdeparted from the spirit of the present invention.

The resonant frequency of the above-mentioned each resonator 3 has twoparallel resonance frequencies and one series resonance frequency. Theparallel resonance frequencies are given as frequencies when theimaginary components of the denominators of Equations 9 and 10 become 0,and are represented by the following Equation 11.

$\begin{matrix}{f_{{reson}\mspace{11mu}\ldots\mspace{11mu}{parallel}} = {\frac{1}{2\pi}\sqrt{\frac{1}{2L_{p}L_{s}}\left( {\left( {\frac{L_{p}}{C_{p}} + \frac{L_{s}}{C_{s}} + \frac{L_{p}}{C_{s}}} \right) - \left( {\left\lbrack {\frac{L_{p}}{C_{p}} + \frac{L_{s}}{C_{s}} + \frac{L_{p}}{C_{s}}} \right\rbrack^{2} \pm \frac{4L_{p}L_{s}}{C_{p}C_{s}}} \right)^{\frac{1}{2}}} \right)}}} & (11)\end{matrix}$

On the other hand, the series resonance frequency is given as afrequency when the numerator of Equations 9 and 10 becomes 0, andrepresented by the following Equation 12.

$\begin{matrix}{f_{{reson}\mspace{11mu}\ldots\mspace{11mu}{series}} = \frac{1}{2\pi\sqrt{L_{s}C_{s}}}} & (12)\end{matrix}$

Here, it is noted that while the alternating voltage of the terminal 101d in Equation 9 has a series resonance point determined by Ls and Cs,the terminal 101 g does not have the series resonance point. Therefore,the reactance component of the terminal 101 d is subject to theattenuation operation by a reactance element with the reverse polarity.As a result, it is understood that the voltage amplitude of the terminal101 g becomes larger than the voltage amplitude of the terminal 101 d atthe entire frequency region before the serial resonance frequency.

FIGS. 5B and 5C show the transition of the alternating voltagecharacteristic and the phase characteristic with respect to thefrequency of the resonator according to the second embodiment when theverification circuit of FIG. 5A is used. In FIG. 5B, reference numeral201 g denotes the amplitude characteristic of an alternating voltage ofthe terminal 1 (101 g) shown in FIG. 5A, and reference numeral 201 ddenotes the amplitude characteristic of an alternating voltage of theterminal 2 (101 d) shown in FIG. 5A. Further, in FIG. 5B, referencenumeral 201 p denotes the phase characteristic of the terminal 1 (101 g)shown in FIG. 5A.

Since the capacitors Cp and Cs have high impedances in a low frequencyregion in FIG. 5B, only the reactance of inductor Lp is seen. Therefore,the polarity of the resonator 3 becomes inductive. Even though thepolarity of the series resonator unit 70 including of the capacitor Csand the inductor Ls is changed from the capacitive to inductive aroundthe serial resonance point, the polarity of the serial resonator unitbecomes capacitive at the serial resonance point.

As the frequency becomes higher, the inductive impedance of the inductorLp becomes equal to the impedance due to a composite capacitor composedof a serial resonator and the capacitor Cp. Therefore, the resonatorcauses the first parallel resonance. The parallel resonance frequency isdenoted by the broken-line 300 shown in (a) and (b) of FIG. 5B (firstresonance point 300).

The series resonance is caused at a frequency that is equal to thereactance of the series resonator unit including the capacitor Cs andthe inductor Ls when the frequency increases from the parallelresonance. After the serial resonance frequency, the series resonatorunit 70 and the resonator 3 become inductive. The series resonancefrequency is denoted by the broken line 301 shown in (a) and (b) of FIG.5B (series resonance point 301).

Finally, at a frequency when a capacitive impedance of the capacitor Cpis equal to a composite inductive impedance of the series resonator unit70 that becomes inductive and the inductor Lp, the second parallelresonance is caused. The parallel resonance frequency is denoted by thebroken line 302 shown in (a) and (b) of FIG. 5B (second parallelresonance point 302). At a frequency after the second parallel resonancefrequency, the resonator 3 is maintained to be capacitive.

The order when the polarity of the resonator is changed into inductiveor capacitive is fixed even if elements that compose the resonator 3have any value. That is, it is understood that the first parallelresonance frequency shown by the first parallel resonance point 300 isalways lower than the series resonance frequency shown by the seriesresonance point 301. Therefore, the oscillator that includes theresonator 3 according to the second embodiment can make the oscillationvoltage amplitude 201 g of the gate terminal larger than the oscillationvoltage amplitude 201 d of the drain terminal when oscillating at thefirst parallel resonance frequency.

By the above-described operation, it is possible to reduce the operatingtime of the transistor in the triode region without adjusting the DCvoltage level of the gate terminal, like the oscillator according to therelated art. Therefore, it is further possible to suppress thedeterioration of the Q-factor that is caused by the decrease of theoutput resistance of the transistor in the triode region.

It is possible to simultaneously satisfy the increase in the oscillationamplitude, the removal of the tail current source (or top currentsource) that serves as the noise source, and reduction of the distortionof the oscillation waveform without deteriorating the Q-factor of theresonator (those are the trade-off in the related art), and thus achievean oscillator that has a low phase noise characteristic.

Moreover, if the following method is adopted, the effect of the secondembodiment can be further improved. The element values of the inductorsLs and Lp, and the capacitors Cs and Cp are adjusted by using thecharacteristic when the resonance points of the above-mentionedresonator 3 are fixed in the order of the parallel resonance point, theseries resonance point, and the parallel resonance point, and the seriesresonance point 301 is arranged close to the first parallel resonancepoint 300. As a result, it is further possible to increase the amplituderatio of the oscillation voltage amplitude 201 g of the gate terminaland the oscillation voltage amplitude 201 d of the drain terminal.

Moreover, the first parallel resonance (frequency) point 300 may beseparated from the second resonance (frequency) point 302 by adjustingthe above-mentioned element values. The loop gain of the oscillator atthe second parallel resonance frequency can become sufficiently smallerthan 1 by setting the second resonance frequency 302 to be larger thanthe cutoff frequency of the transistor that composes the differentialamplifier, and the oscillator can be stably oscillated at the firstresonant frequency 300.

FIG. 5C shows a transfer impedance from the terminal 201 d of theresonator to the terminal 201 g and the driving-point impedance of theterminal 201 d when a resonator has the following element values in theoscillator according to the second embodiment: Cs=70 fF, Cp=70 fF,Ls=125 pH, and Lp=75 pH. Further, in FIG. 5C, reference numeral 211 gdenotes the amplitude characteristic of an alternating voltage of theterminal 1 (101 g) shown in FIG. 5A, and reference numeral 211 d denotesthe amplitude characteristic of an alternating voltage of the terminal 2(101 d) shown in FIG. 5A. In this embodiment, the oscillation voltageamplitude 211 g of the gate terminal can be larger than the oscillationvoltage amplitude 211 d of the drain terminal when oscillating at thefirst parallel resonance frequency.

Moreover, FIG. 6 shows a simulation result of the oscillation voltagewaveform 221 d of the drain terminal, the oscillation voltage waveform221 g of the gate terminal, and the current waveform 231 d of the drainterminal when the resonator 3 having the above-described element valuesis used in the oscillator according to the second embodiment. Theoscillator according to the second embodiment can reduce the operatingtime of the transistor in the triode region by making the voltageamplitude of the drain terminal smaller, without adjusting the DCvoltage level of the gate terminal. Therefore, the Q-factor of theresonator may not be deteriorated.

Therefore, according to the second embodiment, it is possible tosimultaneously satisfy the increase in the oscillation amplitude, theremoval of the noise source, and the reduction of the distortion of theoscillation waveform without deteriorating the Q-factor of theresonator, thereby achieving an oscillator that has a low phase noisecharacteristic.

Third Embodiment

FIG. 7 is a circuit diagram that shows an oscillator according to athird embodiment of the invention. The oscillator according to the thirdembodiment includes a differential amplifier 2, and resonators 3A, 3Beach having inductors Lp and Ls, and capacitors Cp and Cs. Theresonators 3A, 3B include parallel resonator units 60A and 60B thatinclude the inductor Lp and the capacitor Cp installed between terminals102 d 1 and 102 d 2 and terminals 102 g 1 and 102 g 2, and seriesresonator units 80A and 80B that include the capacitor Cs and theinductor Ls in this order as seen from each of the terminals 102 d 1 and102 d 2. The central points of the capacitor Cs and the inductor Ls 2 ofthe series resonator units 80 (80A, 80B) become terminals 102 g. Theoutput terminal of the transistor Q1 that composes the differentialamplifier is connected with an input terminal 102 d 1 of the resonator3A, is output from the terminal 102 g 1 of the series resonator unit 80Aof the resonator 3A and connected to the input terminal of the othertransistor Q2. An output of the transistor Q2 is connected with theresonator 3B, similar to the transistor Q1 and the output of theresonator 3B is output from the terminal 102 g 2 of the series resonatorunit 80B to be connected to the input terminal of transistor Q1. Theparallel resonator units 60A and 60B are provided with power supplydirect connection terminals 102 p 1 and 102 p 2 and second power supplyconnection terminals 102 a 1 and 102 a 2 as connection terminals to thepower supply VDD. The series resonator units 80A and 80B are providedwith connection terminals 102 b 1 and 102 b 2 as connection terminals tothe power supply VDD.

The same verification as that in FIG. 5 of the second embodiment isperformed in order to show the transfer characteristic of the resonator3 that composes the oscillator according to the third embodiment.Equations 13 and 14 represent alternating voltage amplitudes of theterminal 102 d and the terminal 102 g when the alternating currentI_(in) is input from the resonator terminal 102 d of third embodiment.

$\begin{matrix}{V_{d} = {\frac{{\left( {\frac{1}{\omega\; C_{s}} - {\omega\; L_{s}}} \right)} \cdot \frac{L_{p}}{C_{p}}}{{j\left( {\frac{L_{p}}{C_{p}} + \frac{L_{p}}{C_{s}} + \frac{L_{s}}{C_{p}}} \right)} - {j\left( {{\omega^{2}L_{p}L_{s}} + \frac{1}{\omega^{2}C_{p}C_{s}}} \right)}} \cdot I_{i\; n}}} & (13) \\{V_{g} = {\frac{{{\omega\; L_{s}}} \cdot \frac{L_{p}}{C_{p}}}{{j\left( {\frac{L_{p}}{C_{p}} + \frac{L_{p}}{C_{s}} + \frac{L_{s}}{C_{p}}} \right)} - {j\left( {{\omega^{2}L_{p}L_{s}} + \frac{1}{\omega^{2}C_{p}C_{s}}} \right)}} \cdot I_{i\; n}}} & (14)\end{matrix}$

According to Equation 13, the terminal 102 d of the resonator has thesame equation as Equation 9, and the denominator is the same as theresonator 3 of the second embodiment. Therefore, the resonator has twoparallel resonance points and one series resonance point and the orderof the capacitive and the inductivity of the frequency and impedanceappear is the same as the resonator 3 of the second embodiment.

From Equations 13 and 14, after the series resonance frequency, thevoltage amplitude of the terminal 102 g is always larger than thevoltage amplitude of the terminal 102 d. That is, the oscillatoraccording to the third embodiment that has the above-mentioned resonator3 can make the oscillation voltage amplitude of the gate terminal largerthan the oscillation voltage amplitude of the drain terminal whenoscillating at the second parallel resonance point. Therefore, with thiscircuit configuration according to the third embodiment, the phase noisecan be reduced.

Similar to the second embodiment, the element values of the inductors Lsand Lp, and the capacitors Cs and Cp, which compose the resonator 3, areadjusted by using the characteristic that the resonance points of theabove-mentioned resonator 3 are fixed in the order of the parallelresonance point, the series resonance point, and the parallel resonancepoint, and the series resonance point 301 of FIG. 5B is arranged closeto the second parallel resonance point 302. As a result, it is furtherpossible to increase the amplitude ratio of the oscillation voltageamplitude of the gate terminal and the oscillation voltage amplitude ofthe drain terminal.

Moreover, the first parallel resonance point 300 may be separated fromthe second resonance point 302 by adjusting the above-mentioned elementvalues. The alternating voltage values of the terminal 102 g of theresonator 3 are in proportion to the value of Ls and have the smallvalue in the low frequency region. The higher the frequency is, thelarger the alternating voltage values are. Therefore, the first parallelresonance frequency 300 and Ls of the resonator 3 are set such that theloop gain of the oscillator at the first parallel resonance frequency300 is sufficiently smaller than 1, and thus the oscillator can bestably oscillated at the second resonance frequency 302.

FIG. 8 shows a simulation result of frequency characteristic of thealternating voltage amplitude 212 d of the drain terminal 102 d(terminal 1) and the alternating voltage amplitude 212 g of the gateterminal 102 g (terminal 2) when the element values of the resonator inthe oscillator according to the third embodiment are adjusted asfollows: Cs=100 fF, Cp=300 fF, Ls=250 pH, and Lp=150 pH. Therelationship between the alternating voltage amplitude 212 d and thealternating voltage amplitude 212 g of the gate terminal reverses ascompared with the second embodiment (FIG. 5C), and the oscillationvoltage amplitude 212 g of the gate terminal may be larger than theoscillation voltage amplitude 212 d of the drain terminal whenoscillating at the second parallel resonance frequency 302 (about 40 GHzin the example of FIG. 8).

Further, FIG. 9 is a simulation result of the oscillation voltagewaveform 222 d of the drain terminal, the oscillation voltage waveform222 g of the gate terminal, and the oscillation current waveform 232 dof the drain terminal in the oscillator. The oscillator according to thethird embodiment can reduce the operating time of the transistor in thetriode region by making the voltage amplitude of the drain terminalsmaller, without adjusting the DC voltage level of the gate terminal.Therefore, the Q-factor of the resonator does not become deteriorated.

According to the third embodiment, it is possible to simultaneouslysatisfy the increase in the oscillation amplitude, the removal of thenoise source, and the reduction of the distortion of the oscillationwaveform without deteriorating the Q-factor of the resonator, and thusachieve an oscillator that has a low phase noise characteristic.

First Modification

Next, FIG. 10 shows an example of an oscillator that is modified fromthe oscillator according to the third embodiment and includes aresonator 3 in which the inductor Lp of the parallel resonator unit andthe inductor Ls of the series resonator unit are used as differentialinductors. This oscillator is configured such that a gate bias voltageof the transistors Q1 and Q2 is applied from the terminal n-b connectedwith the central point of the inductor Ls of the series resonator unit,and the power supply voltage VDD is applied from the terminal n-pconnected with the central point of the inductor Lp of the parallelresonator unit. With this configuration, it is possible to independentlyset the gate bias voltage from the power supply voltage VDD. As aresult, it is possible to easily design the oscillation frequency of theoscillator and the consumed current.

Fourth Embodiment

FIG. 11 is a circuit diagram showing an oscillator according to a fourthembodiment of the invention. The resonators 4 (4A, 4B) that composes theoscillator is mutually inductively coupled to the inductors Lp and Lsthat composes the resonator 3 of the oscillator according to the secondembodiment.

An output terminal of a transistor Q1 that composes a differentialamplifier 2 is connected with an input terminal 103 d 1 of the resonator4A, and an output of the resonator 4A is output from a terminal 103 g 1and connected with an input terminal of the other transistor Q2. Anoutput of the transistor Q2 is connected to the input terminal 103 d 2of the resonator 4B, similar to the transistor Q1. An output of theresonator 4B is output from the terminal 103 g 2 and connected to theinput terminal of the transistor Q1. The parallel resonator units A andB are provided with power supply direct connection terminals 103 p 1 and103 p 2 and second power supply connection terminals 103 a 1 and 103 a 2as connection terminals to the power supply VDD. The series resonatorunits A and B are provided with connection terminals 103 b 1 and 103 b 2as connection terminals to the power supply VDD.

The frequency characteristic of the resonator 3 will be described withreference to FIGS. 12A, 12B, and 12C. FIG. 12A is a verification circuitdiagram showing the AC characteristic of the resonator 4. Referencenumeral 103 g of FIG. 12B denotes an alternating voltage amplitude ofthe terminal 103 d when the magnitude of an mutual inductance M ischanged in FIG. 12A. Further, reference numeral 213 g of FIG. 12Cdenotes the amplitude characteristic of the alternating voltage of theterminal 1 (103 g) of FIG. 12A, and reference numeral 213 d denotes theamplitude characteristic of the alternating voltage of the terminal 2(103 d) of FIG. 12A.

The following Equations 15 and 16 represent the alternating voltageamplitudes of the terminal 103 d and the terminal 103 g when thealternating current I_(in) is input from the terminal 103 d of FIG. 12A.

$\begin{matrix}{V_{D} = {\frac{\frac{L_{p}}{C_{p}}\left\{ {\frac{1}{{j\omega}\; C_{3}} + {j\;{\omega\left( {L_{s} - \frac{M^{2}}{L_{p}}} \right)}}} \right\}}{{- {\omega^{2}\left( {{L_{s}L_{p}} - M^{2}} \right)}} + \left\{ {\frac{L_{p}}{C_{s}} + {\frac{L_{p}}{C_{p}}\left( {1 - \frac{M}{L_{p}}} \right)} + \frac{L_{s} - M}{C_{p}}} \right\} - \frac{1}{\omega^{2}C_{s}C_{p}}} \cdot I_{i\; n}}} & (15) \\{V_{G} = {\frac{\frac{L_{p}}{C_{p}}\left\{ {\frac{1}{j\;\omega\; C_{s}}\left( {1 - \frac{M}{L_{p}}} \right)} \right\}}{{- {\omega^{2}\left( {{L_{s}L_{p}} - M^{2}} \right)}} + \left\{ {\frac{L_{p}}{C_{s}} + {\frac{L_{p}}{C_{p}}\left( {1 - \frac{M}{L_{p}}} \right)} + \frac{L_{s} - M}{C_{p}}} \right\} - \frac{1}{\omega^{2}C_{s}C_{p}}} \cdot I_{i\; n}}} & (16)\end{matrix}$

Here, M of Equations 15 and 16 indicates the mutual inductance of Ls andLp, and is represented by Equation 17 when using a coupling coefficientK. The coupling coefficient K represents the degree of coupling of themagnetic field of Ls and Lp, and has negative or positive polarityaccording to the direction where magnetic fields are coupled.M=K√{square root over (L _(s) L _(p))} (but, K≦±1)  (17)

According to Equation 17, when the mutual inductance M has a negativevalue, that is, the coupling coefficient is negative, if the capacitorsCp and Cs and the inductors Lp and Ls that compose the resonator 4 havethe same value, the alternating voltage value of the terminal 103 g ofthe resonator 4 is always larger than the voltage of the terminal 101 gof the resonator 3 in the second embodiment. Meanwhile, the alternatingvoltage value of the terminal 103 d is always smaller than the voltageof the terminal 101 d of resonator 3 in the second embodiment regardlessof the positive or the negative value of the mutual inductance M.

That is, the oscillator having the resonator 4 with the same elementvalues as the second embodiment according to the fourth embodiment canincrease the ratio of the gate voltage amplitude value and the drainterminal voltage amplitude value, which is the advantage of theinvention.

The increase in the above-mentioned voltage of the terminal 103 g meansthe increase in the Q-factor of the terminal 103 g. That is, theoscillators according to the fourth embodiment satisfies the fourfactors: (1) increase in oscillation amplitude, (2) increase in Q of aresonator, (3) reduction of the noise factor caused by the thermal noiseof a transistor and a resistor, and (4) lowering of the distortion of anoscillation waveform, which are derived from Equations 1 and 2.

In addition, as shown in FIG. 12B, the resonator with a negative mutualinductance has an effect that expands the frequency between the resonantfrequencies of the first parallel resonance point and the secondparallel resonance point compared with the resonator according to thesecond embodiment that has the same element values of the inductors Lsand Lp, and the capacitors Cs and Cp. With this effect, it is easy todispose the second parallel resonance point in a higher frequency regionthan the cutoff frequency of the transistor, and thus the oscillator canbe stably oscillated at the first parallel resonance frequency.

Moreover, the resonator according to the fourth embodiment uses themutual inductance M by disposing the inductors Lp and Ls close to eachother. Therefore, the two inductors Lp and Ls may be mounted in oneinductor mounting area. As a result, it is possible to reduce an areafor one inductor, and when the inductor is integrated in an IC chip, itresults in low cost.

FIG. 12C shows a transfer impedance from the terminal 103 d of theresonator to the terminal 103 g and the simulation result of thefrequency characteristic of the driving-point impedance of the terminal103 d when the element values of the resonator in the oscillatoraccording to the fourth embodiment are adjusted as follows: Cs=60 fF,Cp=70 fF, Ls=60 pH, Lp=60 pH, and the coupling coefficient K is −0.6. Asshown in FIG. 12C, the oscillator according to the fourth embodiment canimprove the ratio of the gate voltage amplitude value and the drainterminal voltage amplitude value, which is an advantage of theinvention.

Next, with reference to FIGS. 13A and 13B, the effect that reduces themounting area in the IC chip by disposing the inductors Lp and Ls of thepair of resonators to be closer to each other and using the mutualinductance M will be described. First, FIG. 13A shows an example of thelayout when the oscillator shown in FIG. 10 is integrated in the ICchip. As shown in FIG. 13A, the inductor Lp of the resonator is disposedabove the IC chip and the inductor Ls is disposed below the IC chip. Theelements of the resonators or the transistors Q1 and Q2 may be arrangedbetween the inductors Lp and Ls or at the periphery thereof. As anexample, the length L1 of the IC chip is 670 μm and the width W1 is 210μm.

Next, FIG. 13B shows an example of the layout when the oscillator (whichis functionally the same as the oscillator shown in FIG. 10) shown inFIG. 11 is integrated in the IC chip. As shown in FIG. 13B, the usagearea can be reduced by disposing the inductors Lp and Ls of the pair ofresonators in the same area. The capacitor Cs has been achieved by aparasitic capacitor Cgs of the transistor Q1. For example, the length L2of the IC chip is 120 μm, and the width W2 is 105 μm. According to thelayout shown in FIG. 13B that uses the mutual inductance M, the areadecreases to 1/11 of the layout of FIG. 13A, that is, the area issignificantly reduced in the IC chip.

Second Modification

Next, the modification of the fourth embodiment according to theinvention will be described. A resonator 5 that has a negative mutualinductance M of the inductors Lp and Ls of the pair of resonatorsaccording to the fourth embodiment connects a drain terminal having areversed phase of the differential amplifier 2 and the inductor Lp ofone of resonators, and can be easily obtained by positively magneticallycoupling the inductor Lp to the inductor Ls of the other resonator, asshown in FIG. 14.

That is, if the inductors and the capacitors corresponding to theresonator 4A shown in FIG. 11 are denoted by Lsa, Lpa, Csa, and Cpa,respectively, and the inductors and the capacitors corresponding to theresonator 4B are denoted by Lsb, Lpb, Csb, and Cpb, in FIG. 14, theresonator 5 includes inductors Lpa, Lsb, Lsa, and Lpb that aresequentially arranged in the horizontal direction, capacitors Cpa andCpb that are sequentially arranged in the horizontal direction below theinductors, and capacitors Csb and Csa that are arranged in thehorizontal direction below the capacitors Cpa and Cpb. The inductors Lpaand Lsb and the inductors Lsa and Lpb are positively magneticallycoupled. Further, the terminals n-p1, n-p2, n-a1, n-a2, n-d1, n-d2,n-g1, n-g2, n-b1, and n-b2 are connected with the power supply as shownin FIG. 14.

In this modification, the power supply direct connection terminals n-p1and n-p2 are connected with the power supply VDD, and the commonlygrounded terminals of the transistors Q1 and Q2 of the differentialamplifier 2 are directly connected with the ground terminal. Further,the transfer impedance from the input terminals n-d1 and n-d2 of theresonator 5, to which drain terminals of the transistors Q1 and Q2serving as outputs of the differential amplifier 2 are connected, to theoutput terminals n-g1 and n-g2 of the resonator 5, to which inputs ofthe differential amplifier 2 (gate terminals of the transistors Q1 andQ2) is connected, becomes larger than the driving-point impedance of theinput terminals n-d1 and n-d2 at the oscillation frequency. Therefore,during the oscillating operation, the oscillation voltage amplitude Vgof the gate terminals of the transistors Q1 and Q2 becomes large, andthe oscillation voltage amplitude Vd of the drain terminal becomessmall.

Therefore, according to the second modification, it is possible tosimultaneously satisfy the increase in the oscillation amplitude, theremoval of the noise source, and the reduction of the distortion of theoscillation waveform without deteriorating the Q-factor of theresonator, thereby achieving an oscillator that has a low phase noisecharacteristic. It is further possible to significantly reduce the areain the IC chip.

Fifth Embodiment

FIG. 15 is a circuit diagram showing an oscillator according to a fifthembodiment of the invention. Resonators 6 (6A, 6B) that compose theoscillator is configured to be mutually inductively coupled to theinductors Lp and Ls that compose the resonator 3 (3A, 3B) according tothe third embodiment.

An output terminal of the transistor Q1 that composes a differentialamplifier 2 is connected to an input terminal 104 d 1 of the resonator6A, and an output of the resonator 6A is output from the terminal 104 g1 and input to the input terminal of the other transistor Q2. An outputof the transistor Q2 output is input to an input terminal 104 d 2 of theresonator 6B, similar to the transistor Q1, and an output of resonator6B is output from a terminal 104 g 2 and input to the input terminal ofthe other transistor Q1. The parallel resonator units A and B areprovided with power supply direct connection terminals 103 p 1 and 103 p2 and second power supply connection terminals 103 a 1 and 103 a 2 asconnection terminals to the power supply VDD. The series resonator unitsA and B are provided with connection terminals 103 b 1 and 103 b 2 asconnection terminals to the power supply VDD.

The verification similar to that shown by FIG. 12A of the fourthembodiment is performed in order to show the transfer characteristic ofthe resonator 6 that composes the oscillator according to the fifthembodiment. The following Equations 18 and 19 represent alternatingvoltage amplitudes of the terminal 104 d and the terminal 104 g when thealternating current I_(in) is input from the terminal 104 d of theresonator 6 according to the fifth embodiment.

$\begin{matrix}{V_{D} = {\frac{j\;\frac{L_{p}}{C_{p}}\left\{ {{\omega\left( {L_{s} - \frac{M^{2}}{L_{p}}} \right)} - \frac{1}{\omega\; C_{s}}} \right\}}{{- {\omega\left( {{L_{s}L_{p}} - M^{2}} \right)}} + \left\{ {\frac{L_{p}}{C_{s}} + {\frac{L_{p}}{C_{p}}\left( {1 - \frac{M}{L_{p}}} \right)} + \frac{L_{s} - M}{C_{p}}} \right\} - \frac{1}{\omega^{2}C_{s}C_{p}}} \cdot I_{i\; n}}} & (18) \\{V_{G} = {\frac{j\;\frac{L_{p}}{C_{p}}\left\{ {{\omega\left( {L_{s} - \frac{M^{2}}{L_{p}}} \right)} - {\frac{1}{\omega\; C_{s}} \cdot \frac{M}{L_{p}}}} \right\}}{{- {\omega^{2}\left( {{L_{s}L_{p}} - M^{2}} \right)}} + \left\{ {\frac{L_{p}}{C_{s}} + {\frac{L_{p}}{C_{p}}\left( {1 - \frac{M}{L_{p}}} \right)} + \frac{L_{s} - M}{C_{p}}} \right\} - \frac{1}{\omega^{2}C_{s}C_{p}}} \cdot I_{i\; n}}} & (19)\end{matrix}$

Here, M refers a mutual inductance of the inductors Lp and Ls, similarto the fourth embodiment.

If the mutual inductance M is negative, the second term of the numeratorin Equation 19 is changed to be positive. Therefore, the alternatingvoltage value of the terminal 104 g exceeds the voltage of the terminal104 d in a frequency range that is higher than the series resonancefrequency.

Moreover, similarly to the fourth embodiment, the resonator 6 with anegative mutual inductance has an effect that expands the frequencybetween the resonant frequencies of the first parallel resonance point300 and the second parallel resonance point 302 compared with theresonator 3 according to the third embodiment that has the same elementvalues of the inductors Ls and Lp, and the capacitors Cs and Cp. Withthis effect, it is easy to allow the first parallel resonance frequency300 to have a value such that the loop gain of the oscillator issufficiently smaller? than 1 at the first parallel resonance frequency300, as compared with the third embodiment, and thus the oscillator canbe stably oscillated at the second parallel resonance frequency 302.

In the meantime, when the mutual inductance M is positive, the seriesresonance point is generated in the terminal 104 g of the resonator 6.As represented by Equation 17, since the mutual inductance M is notlarger than the inductance of Lp and Ls, a ratio M/Lp of the mutualinductance M and the inductance Lp of the second term of the numeratorin Equation 19 is always 1 or smaller. That is, the value of thenumerator of Equation 19 becomes 0 at a lower frequency than that of thenumerator of Equation 18. This means that the series resonance frequencyof the terminal 104 g is always lower than the series resonancefrequency of the terminal 104 d.

By approaching the series resonance point of the terminal 104 g to thefirst parallel and serial resonance frequencies of the resonator 6 inthe fifth embodiment, the value of the numerator of Equation 19 at thefirst parallel resonance point may be close to 0, and the alternatingvoltage of the terminal 104 d can have very small value. Therefore, itis possible to make the loop gain of the oscillator significantlysmaller than 1 at the first parallel resonance frequency using theelement values of the resonator set as the above and the mutualinductance M, and thus the oscillator can be stably oscillated at thesecond resonance frequency.

FIG. 16 shows the frequency characteristic 214 g of the alternatingvoltage of the terminal 104 g (terminal 1) and the frequencycharacteristic 214 d of the alternating voltage of the terminal 104 d(terminal 2) when the element values of the oscillator according to thefifth embodiment are set as follows: Cs=200 fF, Cp=100 fF, Ls=250 pH,Lp=150 pH, and the coupling coefficient K is 0.3. As shown in FIG. 16,according to the fifth embodiment, even though the difference betweenthe first parallel resonance frequency and the second resonancefrequency does not expand, the difference between the first parallelresonance frequency and the oscillation amplitude of the alternatingvoltage at the second resonance frequency can be enlarged whenconsidering the frequency characteristic 214 g. Therefore, theoscillator can be stably oscillated at the second resonance frequency.

Therefore, according to the fifth embodiment, it is possible tosimultaneously satisfy the increase in the oscillation amplitude, theremoval of the tail current source that serves as the noise source, andthe reduction of the distortion of the oscillation waveform withoutdeteriorating the Q-factor of the resonator, thereby achieving anoscillator that has a low phase noise characteristic.

Sixth Embodiment

FIG. 17 is a circuit diagram showing an oscillator according to a sixthembodiment of the invention. The capacitors and the inductors thatcompose the resonator according to the sixth embodiment are configuredby open stubs and short stubs that are installed in transmission linessuch as a microstrip line or a coplanar waveguide of elements of theresonator. Resonators 7 (7A, 7B) include a parallel resonator unit thatincludes input terminals n-d1 and n-d2, output terminals n-g1 and n-g2that drives a differential amplifier using a voltage, an inductor Lp anda capacitor Cp connected between the input and output terminals, and aserial resonator unit that includes a capacitor Cs and an inductor Lsarranged in this order as seen from the input terminals n-d1 and n-d2.The central point of the capacitor Cs and the inductor Ls of the seriesresonator unit serves as an output terminal. The resonators 7A and 7Bfurther includes power supply direct connection terminals n-p1 and n-p2that are directly connected to the power supply VDD, other connectionterminals n-b1 and n-b2 that are connected to the power supply Vdd, andconnection terminals n-a1 and n-a2 such as power supply that areconnected to an alternating ground point.

The oscillator according to the sixth embodiment has a feedback loopthat connects an output of one of transistors (for example, transistorQ1) that composes the differential amplifier 2 to the input terminal(for example, input terminal n-d1) of one of the resonators (forexample, resonator 7A), and inputs the output terminal (for example,n-g1) of the resonator to the other transistor (for example, transistorQ2) of the differential amplifier.

Further, the inductors Lp and Ls can be achieved by a short stub with atransmission line of the length of λ/4 or less. Furthermore, thecapacitor Cp can be achieved by an open stub with a transmission line ofthe length of λ/4 or less. The capacitor and the inductor may beconfigured by using a parasitic element that is caused in elements suchas a transistor, between elements, or circuit wiring lines.

The oscillator according to the sixth embodiment is configured such thata transfer impedance from the input terminals n-d1 and n-d2 of theresonator 7 to the output terminals n-g1 and n-g2 of the resonator 7 islarger than a driving-point impedance of the input terminals n-d1 andn-d2 at an oscillation frequency. In this case, the input terminals n-d1and n-d2 of the resonator 7 are connected with the drain terminals ofthe transistors Q1 and Q2 that serve as an output of the differentialamplifier 2, and the output terminals n-g1 and n-g2 of the resonator 7are connected with the inputs of differential amplifier 2 (gateterminals of the transistors Q1 and Q2). Further, in order to remove thetail current source (or top current source) that serves as a noisesource, the power supply direct connection terminals n-p1 and n-p2 thatare directly connected to the power supply VDD without interposing thetail current source therebetween are provided as an element for directlyconnecting the inductor Lp of the parallel resonator unit to the powersupply.

Therefore, according to the sixth embodiment, it is possible tosimultaneously satisfy the increase in the oscillation amplitude, theremoval of the noise source, and the reduction of the distortion of theoscillation waveform without deteriorating the Q-factor of theresonator, thereby achieving an oscillator that has a low phase noisecharacteristic.

Seventh Embodiment

The LC cross-coupled oscillator according to the above embodiments issuitable for an oscillator of a transmitter circuit or a receivercircuit in a communication system that includes a transmitter, areceiver, a baseband circuit, and an antenna. Specifically, byintegrating a transmitter or a receiver that includes an oscillatorhaving a resonator with a mutual inductance M that has a negativepolarity of the inductor Lp of the parallel resonator unit and theinductor Ls of the series resonator unit in an IC chip, it is possibleto achieve low power consumption and low cost of a communication systemwith a reduced size. It is further possible to improve the communicationdistance by better low phase noise characteristic (specifically, in amillimeter wave band).

1. An oscillator comprising: a differential amplifier that includes apair of transistors commonly grounded; and a pair of resonators each ofwhich includes a first terminal, a second terminal, and a thirdterminal, wherein each of the resonators is configured by a feedbackloop in which the first terminal, is connected to an output terminal ofone of the transistors of the differential amplifier, and the secondterminal is connected to an input terminal of the other transistor ofthe differential amplifier, wherein, in each of the resonators, atransfer impedance from the first terminal connected to the outputterminal of the one transistor to the second terminal connected to theinput terminal of the other transistor is larger than a driving-pointimpedance of the first terminal at an oscillation frequency, whereineach resonator includes, between the first terminal and a power supplyterminal, a parallel resonator unit in which an inductor and a capacitorare connected in parallel and a series resonator unit in which aninductor and a capacitor are connected in series, wherein a centralpoint of the inductor and the capacitor of the series resonator unit ofeach resonator is configured as the second terminal of the resonator,and wherein each resonator includes the series resonator unit in whichthe inductor and the capacitor are connected in series in this order asseen from the first terminal, between the first terminal and the powersupply terminal.
 2. The oscillator according to claim 1, whereinterminals of the differential amplifier that are commonly grounded aredirectly connected to a ground terminal.
 3. The oscillator according toclaim 1, wherein the third terminal of each resonator is directlyconnected to the power supply terminal.
 4. The oscillator according toclaim 1, wherein one of the first terminal and the second terminal ofeach resonator is configured to be an output terminal.
 5. The oscillatoraccording to claim 1, wherein each resonator includes a power supplyconnection terminal that directly connects the inductor of the parallelresonator unit to the power supply, as the third terminal.
 6. Theoscillator according to claim 1, wherein the inductor of the seriesresonator unit and the inductor of the parallel resonator unit of eachresonator are mutually inductively connected.
 7. The oscillatoraccording to claim 6, wherein a mutual inductance of the inductor of theseries resonator unit and the inductor of the parallel resonator unit isnegative.
 8. The oscillator according to claim 6, wherein the inductorof the series resonator unit of one of the resonators is connected to adrain terminal having a reversed phase of the differential amplifier,and wherein the inductor of the series resonator unit is positivelymagnetically coupled to the inductor of the parallel resonator unit ofthe other resonator.
 9. An oscillator comprising: a differentialamplifier that includes a pair of transistors commonly grounded; and apair of resonators each of which includes a first terminal, a secondterminal, and a third terminal, wherein each of the resonators isconfigured by a feedback loop in which the first terminal is connectedto an output terminal of one of the transistors of the differentialamplifier, and the second terminal is connected to an input terminal ofthe other transistor of the differential amplifier, wherein, in each ofthe resonators, a transfer impedance from the first terminal connectedto the output terminal of the one transistor to the second terminalconnected to the input terminal of the other transistor is larger than adriving-point impedance of the first terminal at an oscillationfrequency, wherein each resonator includes, between the first terminaland a power supply terminal, a parallel resonator unit in which aninductor and a capacitor are connected in parallel and a seriesresonator unit in which an inductor and a capacitor are connected inseries, wherein the inductor of the series resonator unit and theinductor of the parallel resonator unit are configured as differentialinductors, wherein a central point of the inductor and the capacitor ofthe series resonator unit of each resonator is connected to the inputterminal of the pair of transistors, wherein the central point of theinductor of the parallel resonator unit of each resonator is connectedto the power supply terminal, and wherein each resonator includes theseries resonator unit in which the inductor and the capacitor areconnected in series in this order as seen from the first terminal,between the first terminal and the power supply terminal.
 10. Anoscillator comprising: a differential amplifier that includes a pair oftransistors commonly grounded; and a pair of resonators each of whichincludes a first terminal, a second terminal, and a third terminal,wherein each of the resonators is configured by a feedback loop in whichthe third terminal is connected to a power supply terminal, the firstterminal is connected to an output terminal of one of the transistors ofthe differential amplifier, and the second terminal is connected to aninput terminal of the other transistor of the differential amplifier,wherein each of the resonators comprises, between the first terminal andthe power supply terminal: a parallel resonator unit in which aninductor and a capacitor are connected in parallel; and a seriesresonator unit in which an inductor and a capacitor are connected inseries; wherein terminals of the differential amplifier that arecommonly grounded are connected to a ground terminal, wherein a centralpoint of the inductor and the capacitor of the series resonator unit ofeach resonator is configured as the second terminal of the resonator,and wherein each resonator includes the series resonator unit in whichthe inductor and the capacitor are connected in series in this order asseen from the first terminal, between the first terminal and the powersupply terminal.
 11. The oscillator according to claim 10, wherein theinductor of the series resonator unit and the inductor of the parallelresonator unit of each resonator are mutually inductively connected. 12.The oscillator according to claim 11, wherein the capacitor and theinductor are configured by an open stub and a short stub that compose atransmission line of the resonators.
 13. The oscillator according toclaim 11, wherein the differential amplifier and the resonators areformed in an IC chip, and wherein the inductor of the series resonatorunit and the inductor of the parallel resonator unit that are mutuallyinductively coupled are arranged in the same area of the IC chip. 14.The oscillator according to claim 11, wherein, in each of theresonators, a transfer impedance from the first terminal connected tothe output terminal of the one transistor to the second terminalconnected to the input terminal of the other transistor is larger than adriving-point impedance of the first terminal at an oscillationfrequency.
 15. A communication system comprising: a transmitter circuit;a receiver circuit; a baseband circuit; and an antenna, wherein at leastone of the transmitter circuit and the receiver circuit includes anoscillator, wherein the oscillator comprises: a differential amplifierthat includes a pair of transistors commonly grounded; and a pair ofresonators that includes a first terminal, a second terminal, and athird terminal, wherein each of the resonators is configured by afeedback loop in which the third terminal is connected to a power supplyterminal, the first terminal is connected to an output terminal of oneof the transistors of the differential amplifier, and the secondterminal is connected to an input terminal of the other transistor ofthe differential amplifier, wherein, in each of resonators, a transferimpedance from the first terminal connected to the output terminal ofthe one transistor to the second terminal connected to the inputterminal of the other transistor is larger than a driving-pointimpedance of the first terminal at an oscillation frequency, whereinterminals of the differential amplifier that are commonly grounded areconnected to the ground terminal, wherein each resonator includes,between the first terminal and a power supply terminal, a parallelresonator unit in which an inductor and a capacitor are connected inparallel and a series resonator unit in which an inductor and acapacitor are connected in series, wherein a central point of theinductor and the capacitor of the series resonator unit of eachresonator is configured as the second terminal of the resonator, andwherein each resonator includes the series resonator unit in which theinductor and the capacitor are connected in series in this order as seenfrom the first terminal, between the first terminal and the power supplyterminal.
 16. The communication system according to claim 15, whereinthe differential amplifier and the resonators are formed in an IC chip,and wherein the inductor of the series resonator unit and the inductorof the parallel resonator unit that are mutually inductively coupled arearranged in the same area of the IC chip.